Relational Concept Bottleneck Models

TL;DR

Relational Concept Bottleneck Models (R-CBMs) are proposed, a family of relational deep learning methods providing interpretable task predictions and able to withstand demanding settings including out-of-distribution scenarios, limited training data regimes, and scarce concept supervisions.

Abstract

The design of interpretable deep learning models working in relational domains poses an open challenge: interpretable deep learning methods, such as Concept Bottleneck Models (CBMs), are not designed to solve relational problems, while relational deep learning models, such as Graph Neural Networks (GNNs), are not as interpretable as CBMs. To overcome these limitations, we propose Relational Concept Bottleneck Models (R-CBMs), a family of relational deep learning methods providing interpretable task predictions. As special cases, we show that R-CBMs are capable of both representing standard CBMs and message-passing GNNs. To evaluate the effectiveness and versatility of these models, we designed a class of experimental problems, ranging from image classification to link prediction in knowledge graphs. In particular we show that R-CBMs (i) match generalization performance of existing relational black-boxes, (ii) support the generation of quantified concept-based explanations, (iii) effectively respond to test-time interventions, and (iv) withstand demanding settings including out-of-distribution scenarios, limited training data regimes, and scarce concept supervisions.

Figures (5)

• Figure 1: Relational Concept Bottleneck Models can correctly predict and explain Bart's (B) citizenship by considering Homer's (H) citizenship and his status as Bart’s parent.
• Figure 2: The graph represents the dependencies among the atoms. Here, the atom $p_4(b)$ can be predicted either from the orange $[p_3(b),p_2(a,b),p_1(b,a)]$ or violet $[p_1(b,c),p_2(c,b)]$ tuples of neighbours.
• Figure 3: In R-CBMs (i) the atom encoder $g$ maps input entities to a set of ground atoms (red/green indicate the ground atom label false/true), (ii) the relational bottleneck guides the selection of concept atoms by considering all the possible variable substitutions in $\Theta$, (iii) the atom predictor $f$ maps the selected atoms into a task prediction, and (iv) the aggregator $\oplus$ combines all evidence into a final task prediction.
• Figure 4: Model generalization on Hanoi OOD on the number of disks. Only R-CBMs are able to generalize effectively to settings larger than the ones they are trained on.
• Figure 5: Distribution of class prediction uncertainty comparing CBMs using relational vs propositional bottlenecks.

Theorems & Definitions (5)

• Example 3.1
• Definition 3.2: Learning Problem
• Definition 3.3: Templetized relational concept bottleneck
• Example 3.4
• Example 3.5